Welcome to Part Two in this series about teaching math to ELLs!

## Word Banks and Anchor Charts

*Cindy Garcia has been a bilingual educator for 17 years and is currently a districtwide specialist for bilingual/ESL mathematics. She is active on Twitter @CindyGarciaTX and on *her blog:

One of the most effective strategies to use with English-language learners in the math classroom is to teach students the language of mathematics. While the computation or numbers *might* look similar across much of the world, the way math is talked about may be different.

It is important to reflect on phrases that are commonly used and think about whether or not they make sense. For example, if you are adding using the standard algorithm and you say *add the numbers up, *some students could be confused. When using the standard algorithm, you are usually actually adding the numbers from top to bottom. It is important to use precise language when facilitating math instruction.

Using manipulatives, both physical and virtual, provide students tools to process their thinking. As they use manipulatives, they are making something abstract more tangible. When they need to talk about the math involved, they can literally hold it in their hands and use that to make connections to what they are trying to explain.

Word banks that show Tier 3 vocabulary and a picture or example of the word can be beneficial to students because they have a quick reference that they can use during their math task. Word banks in the mathematics classroom should be organized by concept. Word banks should be easy to read and easily accessible to students in order for them to actually use the word banks.

Constructing classroom anchor charts with students provides the opportunity for the class to synthesize what they have learned and have one place where the main points of a concept are summarized. Their visuals can then be referenced by students when they are stuck, are unsure, or just need a reminder.

The Three Reads strategy can be impactful in helping students make sense of what they have read without relying on tricks such as key words. During the first read, students read the problem or task and focus on the context of the problem. The goal is for them to visualize what is taking place and understand the situation. The second time that students read they are focusing on determining what the question is asking. What is supposed to be solved? What are they supposed to determine? During the third read, students can now focus on what the numbers mean. They should be beyond trying to do calculations and should be able to see the relationship between the numbers and the connections to the task context. Using Three Reads helps students chunk information and allows for more effective processing time.

The best way support students learn in the math classroom is to provide consistent and daily opportunities for SWIRL. The more that students speak, write, interact, read, and listen in the math classroom, the more they will make meaning of the math concepts.

## ‘Equity Moves’

*Ivannia Soto, Theodore Sagun, and Michael Beiersdorf are authors of a forthcoming book by Corwin Press called *Equity Moves to Support Multilingual Learners in Mathematics and Science*. Ivannia Soto is a professor of education at Whittier College, where she is also the director of graduate programs; Theodore Sagun is the director of mathematics instruction and learning at the University of California, Los Angeles,’ community programs and a faculty adviser within the teacher education program; and Michael Beiersdorf is the administrative coordinator of the micro-credentialing program in the Los Angeles Unified school district:*

In this blog, we introduce a term we’ve coined “equity moves,” which are specific language scaffolds—vocabulary, discourse, modes of representation, and text features. These four equity moves can be used in mathematics classrooms to support the rigorous content that multilingual learners (MLLs) encounter every day. The equity moves are defined briefly below and are further contextualized with mathematics examples.

**Vocabulary **– MLLs often bring to the table rich vocabulary in their primary language, so we emphasize the teaching of cognates as an assets-based approach to teaching vocabulary, as well as strategies such as the Frayer model.

For the Frayer model, we select five thematic or larger concept Tier 2 (high-frequency) or Tier 3 (discipline-specific) words. The Frayer model itself consists of a graphic organizer with four quadrants labeled “Example” (lower left), “Nonexample” (lower right), “Visual” (upper right), and “Definition” (upper left). With MLLs, we complete the graphic organizer in a counterclockwise manner, beginning in the lower-left quadrant with “Examples.”

During a recent lesson on the target word “ratio,” students developed Examples by engaging in a common, hands-on, real-life experience. We showed them food menus with prices that naturally generated examples of ratios like, “The cost is $9 for 3 tacos.” Once Examples were generated, we continued to Nonexamples like, “The ratio of price to tacos is 3:9.” From there, Visuals might include pictures of 3 tacos and a sign of $9. Finally, for the Definition, we provided the sentence frame, “A ratio is _____ , _____ , and _____ because _____ .”

**Discourse **– The person doing the most talking is doing the most learning. With the discourse strategies highlighted, we try to disrupt silence in mathematics classrooms.

One common equity move used in mathematics classrooms is providing students opportunities to use their primary language to communicate ideas as well as make sense of and engage with others’ ideas. When MLL students are validated for their primary language and allowed to use it in classrooms, they will more likely feel that they are a full member of the classroom community. Inviting students to use their primary language through partner discussions, such as think-pair-share, or during whole-class discussions, is a great way for students to build mathematics knowledge while also seeing their primary language as a resource for learning.

**Modes of Representation **– This refers to how information or knowledge is stored or encoded in memory. We specifically focus on Bruner’s (1966) three modes of representation:

o Enactive representation (action-based)

o Iconic representation (image-based)

o Symbolic representation (language-based)

One common equity move we use in our mathematics instruction to support action-based, enactive representation is the scaffold of contextualization with manipulatives.

An example of contextualization with manipulatives is allowing students to use base 10 blocks to make sense of numbers. In a recent lesson, our students used base 10 blocks to talk about and make sense of quantities. In this lesson, students counted the quantities of base 10 blocks in their collection (the representation of unit squares), which gave them the opportunity to use their language, understanding of numbers, and the ways quantities can be represented. They worked with classmates to develop their language of numbers, group quantities in ways that made sense to them, made connections to algebraic ideas, and even generated mathematical expressions and equations that described various quantities (Franke et al., 2018).

**Text Features **– Text features are used to help navigate and locate specific information provided in an expository text in an easier and more efficient manner. Teaching students to move through text features can assist them with accessing background knowledge related to the content (Honig, Diamond, & Gutloh, 2000).

Within expository texts, we can engage students with text components such as pictures, diagrams, labels, headings, and content within the text that might be helpful in building understanding and providing greater focus to mathematics. One equity move we use in our mathematics classrooms is calling attention to pictures and images and inviting students to notice and wonder about the media they’re engaging with. As students engage with visuals, we have a great opportunity to support student discussion around pertinent mathematics that the visuals represent.

## Understanding ‘Cultural Differences’

*Kimiko Shibata is a MLL resource teacher for the Waterloo Region District School Board in Canada:*

When planning for instruction, it is important to consider possible cultural differences in mathematics instruction and understanding, especially when working with recently arrived newcomer students.

For example, students may need explicit instruction in number formation if they have learned to write numbers using a different system. Mathematical operations are often formatted and taught differently around the world. The use of decimals, spaces, and commas to help represent place value look different in different countries. Some school systems make use of hands-on math manipulatives such as base 10 blocks, while others do not. Some school systems place more emphasis on rote memory and finding one correct answer, while others place more emphasis on open-ended problem-solving and processes over results. Word problems may not be introduced in early grades in all countries, and topics such as geometry, estimation, or data management may not be introduced in early grades. Our instruction may need to be adapted based on the backgrounds and prior experiences of our students.

Having an educator with qualifications in teaching multilingual learners conduct a thorough mathematics assessment is a must in any initial assessment of a newcomer, as it can provide the classroom teacher(s) with valuable information and insight into the student’s prior knowledge and understandings, strengths, and next steps for instruction. ESL-qualified educators can also be important partners in planning for the instruction of multilingual learners in all content areas.

All educators are teachers of academic language. All students benefit from their educators taking time to explicitly teach the academic language of their subject areas. The Frayer Model is a popular vocabulary teaching strategy that can be used in the mathematics classroom and involves students filling in a graphic organizer with the key vocabulary word, examples, and nonexamples, as well as definitions, facts, illustrations, or characteristics of the key word.

The Picture Word Induction Model is another excellent tool for teaching mathematics vocabulary and concepts. Labeling photographs of real-life items taken by the teacher or by students themselves can lead to high interest and engagement (e.g., a photo of cases of pop with price tags shown at the grocery store for estimation and multiplication/division discussions, a photo of geometric shapes and 3D solids found on the school playground to learn the names and attributes of geometric shapes and solids, etc.). It’s relatively easy to findimages online that are free to use for classroom purposes.

As with any content area, the use of visuals is key for multilingual learners in mathematics classrooms and can benefit all students. Educators can use visual monolingual or dual-language vocabulary cards to help support an understanding of key mathematics vocabulary, and students can benefit from using either physical math manipulatives orvirtual math manipulativesto support their comprehension of vocabulary and concepts. Video content can often be very helpful for multilingual learners (even just a quick recording of the teacher explaining a concept). When video content is uploaded to YouTube, the speed of the video can be slowed down as needed, and automatedtranslated closed captioning can be turned on to support comprehension.

Visual problem-solving and visual math talks can help all students to better access concepts and vocabulary and are often particularly accessible for multilingual learners, especially those who may not be fully literate in their home languages (and are therefore not able to benefit from translated questions). It is important to note that even students who are fully literate in a home language may struggle with translated math questions, as not all vocabulary and sentence structures will translate well.

I’m a huge fan of encouraging students to leverage their home languages when possible to help them learn academic vocabulary and curriculum content in the mathematics classroom, including using translation tools as needed and discussing and solving math problems in groups with other students who speak the same home language. Encouraging the use of home languages in the classroom can provide equitable access to new learning, helps to facilitate connections between languages, and positively impacts understanding, participation, and student engagement.

It is good to remember that strategies that support content-area vocabulary acquisition for multilingual learners will also support other students in the class as they learn the language of mathematics. Learning how to better support multilingual learners makes us better teachers of all students.

Thanks to Cindy, Ivannia, Theodore, Michael, and Kimiko for contributing their thoughts!

The new question of the week is:

*What instructional strategies do you recommend using with English Language Learners in math classes?*

In Part One, Isabel Becerra, Beth Skelton, Tan Huynh, and Jim Ewing contributed their suggestions.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected]. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo.

Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching.

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